0=2k^2-27k+81

Solution for 0=2k^2-27k+81 equation:

0=2k^2-27k+81

We move all terms to the left:

0-(2k^2-27k+81)=0

We add all the numbers together, and all the variables

-(2k^2-27k+81)=0

We get rid of parentheses

-2k^2+27k-81=0

a = -2; b = 27; c = -81;
Δ = b2-4ac
Δ = 272-4·(-2)·(-81)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9}{2*-2}=\frac{-36}{-4}
=+9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9}{2*-2}=\frac{-18}{-4}
=4+1/2
$